$1..$ For the circuit given below

a$)(25$ pts$).$ Connect inputs $V_{\text{I}\text{N}\text{A}},V_{\text{I}\text{N}\text{B}}$ together and find voltage transfer characteristics $($VTC$),$

b$)(25$ pts$).$ Apply some suitable time waveforms to inputs to prove its logical function. $($ Use LTspice or PSpice for your analysis.$)$

$($Choose the values of $R_{BA}$ and $R_{BB}$ specific to your student ID number. Two rightmost digits of your ID to be added to $40k.$ For example if your ID is $20070005037$ your resistors values will be $40037.)$

FIGURE P$10\mathrm{.}2454$L$02/74$L$02$ LTTL NOR Gate